A most representative design of such brake booster unit represents a housing comprising a front and a rear shell element mechanically coupled with each other and holding firmly a pneumatically operated resilient membrane by squeezing therebetween the outer periphery of the latter. By the provision of this membrane, the interior space of the housing is divided into two chambers, one being the vacuum chamber fluidically connected with a suction manifold of a drive internal combustion engine, the other being the atmospheric pressure chamber kept in fluid communication with ambient atmosphere. The root or inner periphery of the said diaphragm is mounted, in this case, in a recess formed on the rod portion of a power piston. In such a conventional arrangement, however, when the operative air pressure differential between the chambers is applied to the diaphragm it is liable to disengage radially from position. In addition, the related parts of the unit, with the attached portion of the diaphragm, must be fabricated and tightly assembled together to a high precision for tight fitting of the diaphragm for establishing enough airtight attachment of the latter in position.